< σ and σ ∩ σ ′ < σ ′ ;\n\nN R = σ\n\n∪ ⋅ ⋅ ⋅ ∪ σ t .\n\nA rational simplicial complete d -dimensional fan Σ deﬁnes a d -dimensional toric variety P d Σ having only orbifold singularities which we assume to be projective. Moreover, T ∶ = N ⊗ Z C ∗ ≃ ( C ∗ ) d is the torus action on P d Σ . We denote by Σ ( i ) the i -dimensional cones\n\nFor a cone σ ∈ Σ, ˆ σ is the set of 1-dimensional cone in Σ that are not contained in σ\n\nand x ˆ σ ∶ = ∏ ρ ∈ ˆ σ x ρ is the associated monomial in S .\n\nDeﬁnition 2.2. The irrelevant ideal of P d Σ is the monomial ideal B Σ ∶ =< x ˆ σ ∣ σ ∈ Σ > and the zero locus Z ( Σ ) ∶ = V (